This repository provides mathematical validation and test coverage. It does NOT constitute a production-ready cryptographic library.
A mathematical validation and audit package for Shamir Secret Sharing.
See the formal validation report in reports/validation.md.
Shamir Secret Sharing is based on Lagrange interpolation at x=0.
Given secret (S \in \mathbb{F}), threshold (t), and polynomial:
[ f(x) = S + a_1 x + a_2 x^2 + \dots + a_{t-1} x^{t-1} ]
Shares: ((x_i, y_i)) with (y_i = f(x_i)).
Reconstruction at (x=0) uses Lagrange interpolation:
[ S = \sum_{i=1}^{t} y_i \cdot \prod_{\substack{j=1 \ j \neq i}}^{t} \frac{-x_j}{x_i - x_j} ]
Implemented in Python 3.x and JavaScript with deterministic RNG. Deterministic RNG is used exclusively for reproducible validation and MUST NOT be used in production environments.
Automated validation runs across multiple seeds: [1337, 42, 2025, 9001, 314159].
Reports are generated in Markdown (summary.md) and HTML (summary.html).
Please use the following Bitcoin address for bounty distribution: bc1q4fv9w2pwpgqyp0gzt20c6n6m4mxs9yga2qgm9f This address is provided for voluntary research support only.
- Define finite field explicitly (GF(p) or GF(2^n))
- Enforce uniqueness and validity of x-coordinates
- Use cryptographically secure RNG for coefficients
- Add metadata (field, threshold, index, checksum/MAC) to shares
- Implement constant-time field operations
This project is licensed under the MIT License – see the LICENSE file for details.